%?KALMANF?-?updates?a?system?state?vector?estimate?based?upon?an
%???????????observation?using?a?discrete?Kalman?filter.
%
%?Version?1.0?June?30?2004
%
%?This?tutorial?function?was?written?by?Michael?C.?Kleder
%
%?INTRODUCTION
%
%?Many?people?have?heard?of?Kalman?filtering?but?regard?the?topic
%?as?mysterious.?While?it‘s?true?that?deriving?the?Kalman?filter?and
%?proving?mathematically?that?it?is?“optimal“?under?a?variety?of
%?circumstances?can?be?rather?intense?applying?the?filter?to
%?a?basic?linear?system?is?actually?very?easy.?This?Matlab?file?is
%?intended?to?demonstrate?that.
%
%?An?excellent?paper?on?Kalman?filtering?at?the?introductory?level
%?without?detailing?the?mathematical?underpinnings?is:
%?“An?Introduction?to?the?Kalman?Filter“
%?Greg?Welch?and?Gary?Bishop?University?of?North?Carolina
%?http://www.cs.unc.edu/~welch/kalman/kalmanIntro.html
%
%?PURPOSE:
%
%?The?purpose?of?each?iteration?of?a?Kalman?filter?is?to?update
%?the?estimate?of?the?state?vector?of?a?system?（and?the?covariance
%?of?that?vector）?based?upon?the?information?in?a?new?observation.
%?The?version?of?the?Kalman?filter?in?this?function?assumes?that
%?observations?occur?at?fixed?discrete?time?intervals.?Also?this
%?function?assumes?a?linear?system?meaning?that?the?time?evolution
%?of?the?state?vector?can?be?calculated?by?means?of?a?state?transition
%?matrix.
%
%?USAGE:
%
%?s?=?kalmanf（s）
%
%?“s“?is?a?“system“?struct?containing?various?fields?used?as?input
%?and?output.?The?state?estimate?“x“?and?its?covariance?“P“?are
%?updated?by?the?function.?The?other?fields?describe?the?mechanics
%?of?the?system?and?are?left?unchanged.?A?calling?routine?may?change
%?these?other?fields?as?needed?if?state?dynamics?are?time-dependent;
%?otherwise?they?should?be?left?alone?after?initial?values?are?set.
%?The?exceptions?are?the?observation?vectro?“z“?and?the?input?control
%?（or?forcing?function）?“u.“?If?there?is?an?input?function?then
%?“u“?should?be?set?to?some?nonzero?value?by?the?calling?routine.
%
%?SYSTEM?DYNAMICS:
%
%?The?system?evolves?according?to?the?following?difference?equations
%?where?quantities?are?further?defined?below:
%
%?x?=?Ax?+?Bu?+?w??meaning?the?state?vector?x?evolves?during?one?time
%??????????????????step?by?premultiplying?by?the?“state?transition
%??????????????????matrix“?A.?There?is?optionally?（if?nonzero）?an?input
%??????????????????vector?u?which?affects?the?state?linearly?and?this
%??????????????????linear?effect?on?the?state?is?represented?by
%??????????????????premultiplying?by?the?“input?matrix“?B.?There?is?also
%??????????????????gaussian?process?noise?w.
%?z?=?Hx?+?v???????meaning?the?observation?vector?z?is?a?linear?function
%??????????????????of?the?state?vector?and?this?linear?relationship?is
%??????????????????represented?by?premultiplication?by?“observation
%??????????????????matrix“?H.?There?is?also?gaussian?measurement
%??????????????????noise?v.
%?where?w?~?N（0Q）?me

?屬性????????????大小?????日期????時間???名稱
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?????文件???????4326??2010-12-12?05:46??ukf.m

?????文件???????7652??2012-02-28?11:24??kalmanf.m

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